Empirical Exercise 6: Discrimination
London School of Economics and Political Science
February 16, 2026
Today: what if the treatment itself is time-invariant?
Three competing views:
The debate hinges on identification
\[\begin{align*} \log(\text{wage}_{it}) = \beta_{0} &+ \beta_{1}\mathbb{1}[\text{race}_{i} = \text{African American}] \\ &+ \beta_{2}\text{education}_{it} + \beta_{3}\text{experience}_{it} + e_{it} \end{align*}\]
\[\Delta\log(\text{wage}_{it}) = \beta_{1}\underbrace{\Delta\mathbb{1}[\text{race}_{i}]}_{= \, 0} + \beta_{2}\Delta\text{education}_{it} + \beta_{3}\Delta\text{experience}_{it} + \Delta e_{it}\]
Four resumes per ad: one high + one low quality per racial group
| Dimension | High Quality | Low Quality |
|---|---|---|
| Experience | More years | Less experience |
| Skills | Computer skills | Basic skills only |
| Certifications | External certifications | None |
| Extras | Volunteering, email address | Employment gaps |
\[\mathbb{E}\left[e_{it} \mid \mathbb{1}[\text{race}_{i}]\right] = 0\]
Names are randomly assigned — all characteristics balanced. Simple regression gives a causal estimate. No controls needed.
| Variable | White mean | African-American mean | p-value |
|---|---|---|---|
| Years of experience | 7.86 | 7.83 | 0.85 |
| University education | 0.72 | 0.72 | 0.61 |
| Computer skills | 0.81 | 0.83 | 0.03 |
| Special skills | 0.33 | 0.33 | 0.83 |
| Volunteer work | 0.41 | 0.41 | 0.68 |
| Work in school | 0.56 | 0.56 | 0.84 |
| Employment holes | 0.45 | 0.45 | 0.77 |
| Military experience | 0.09 | 0.10 | 0.27 |
| Number of jobs | 3.66 | 3.66 | 0.86 |
The difference is 3.20 percentage points — equivalent to approximately 8 years of additional experience.
\[\widehat{\mathbb{1}[\text{callback}]}_{i} = \underset{(0.0055)}{0.0965} - \underset{(0.0078)}{0.0320} \cdot \mathbb{1}[\text{race}_{i} = \text{African American}]\]
\(\hat{\beta}_{0} = 0.0965\) is the White callback rate.
When the African-American indicator equals zero, the predicted callback rate equals the intercept.
\(\hat{\beta}_{0} + \hat{\beta}_{1} = 0.0645\) is the African-American callback rate.
The coefficient measures the racial gap: \(-0.0320\) or \(-3.20\) percentage points.
No controls needed — randomisation ensures \(\text{Cov}(\mathbb{1}[\text{race}_{i}], e_{i}) = 0\).
\[\hat{\beta}_{1} = \bar{y}_{\text{African American}} - \bar{y}_{\text{White}} = 0.0645 - 0.0965 = -0.0320\]
| Observational + Panel | Experiment | |
|---|---|---|
| Identification | OVB: skills confound race | \(\mathbb{E}[e_{it} \mid \text{race}_{i}] = 0\) by design |
| Time-invariant treatment | FD eliminates the variable of interest | Randomisation sidesteps the problem |
| Controls | Never fully resolve confounding | Not needed |
Randomisation solves what panel data cannot
White low-quality applicants (8.50%) receive more callbacks than African-American high-quality applicants (6.70%).
“Lexicographic search” — employers may stop reading at African-American names
No class next week — reading week.
After reading week: finishing Topic 8 with differences-in-differences.